Quaternary phase shift keying (QPSK) is a method of amplitude-modulating a data stream dk(t) into orthogonal in-phase d1(t) and quadrature dQ(t) data streams onto the cosine and sine functions of a carrier wave. The pulse stream d1(t) amplitude-modulates the cosine function with an amplitude of +1 or −1. This is equivalent to shifting the phase of the cosine function by 0 or π, producing a binary PSK waveform. The pulse stream dQ(t) similarly modulates the sine function and yields a binary PSK waveform orthogonal to the cosine function. The summation of these two orthogonal data streams of the carrier wave yields the QPSK waveform.
In QPSK, for a pulse duration of T, each of the data streams have a pulse duration of 2T, the odd and even streams are each transmitted at a rate of ½ T bit/second, and every other transition of one pulse stream (I or Q) aligns with the alternate pulse stream (Q or I). Because of this alignment, the carrier phase can only change once every 2T. At every other phase change of the carrier, or every 4T, both pulses change sign at the same transition, yielding a carrier phase change of 180°. When a QPSK waveform is filtered to reduce spectral sidelobes, these 180° phase shifts cause the carrier waveform envelope to momentarily collapse (i.e., to go to zero). When the waveform is restored, such as in satellite communications using non-linear amplifiers, all of the undesirable sidelobes are also restored, which can interfere with nearby channels and other communications systems.
Offset QPSK (OQPSK), also known as staggered QPSK (SQPSK), is a modification of QPSK in that the timing of the pulse streams dI(t) and dQ(t) is shifted such that the alignment of the two streams is offset by the pulse duration T. This staggering prevents both streams from incurring a phase change at the same time, and the waveform envelope is thereby prevented from collapsing to zero. When an OQPSK signal is bandlimited, the resulting intersymbol interference (ISI) tends to cause the envelope to droop in the region of □ 90° phase transitions, but the envelope does not go to zero. When the bandlimited OQPSK signal passes through a non-linear transponder, the envelope droop is removed and the high frequency component associated with the collapse of the envelope will not be reinforced, avoiding out-of-band interference.
Minimum shift keying (MSK) may be considered a special case of OQPSK in that out-of-band interference is suppressed (as in OQPSK) but sinusoidal bit weighing is used to eliminate discontinuous phase transitions. The MSK waveform has a constant amplitude envelope with phase continuity in the RF carrier at the bit transitions. Gaussian MSK (GMSK) is the filtered or smoothed version of the MSK in which the smoothing filter is Gaussian. Quadrature amplitude modulation (M-ary QAM of M-ary PSK) also consists of two independently amplitude-modulated data streams in quadrature, but instead of a binary alphabet with two states per channel symbol period, there are M states or transitions allowing the transmission of k=log2M bits during each symbol period. Each block of k data bits is split into two (k/2) bit blocks. At the receiver, each of the two data streams is independently detected using matched filters.
Smoothing is desirable. It is accomplished using a root raised cosine (RRC) filter or Gaussian filter (as in GMSK), for example. This smoothing or pulse shaping smears each symbol to adjacent symbols. This interference is known as intersymbol interference (ISI), and is generally undesirable. In the case of a RRC filter, a RRC filter matched filter at the demodulator removes all ISI introduced by the RRC pulse shaping filter, thus restoring the symbols. This is not the case for Gaussian filters. Furthermore, band limiting analog circuits, anti-aliasing filters, etc., could also introduce ISI which cannot be restored easily (without proper equalization), even with a RRC matched filter. ISI affects timing error detection. This problem is particularly evident in GMSK even in the presence of equalization filters.
Each of the above waveforms (OQPSK, MSK and GMSK) are characterized by continuous phase modulation (CPM). It is understood that the concepts described herein apply not only to CPM, but to any modulation with phase coherent demodulation, such as QAM or QPSK with ISI. It is desirable to smooth the waveform in the time domain to concentrate a signal's energy in a narrower bandwidth, thereby increasing bandwidth efficiency by allowing adjacent signals to be packed closer together. However, that smoothness produces ISI and tends to obscure or eliminate the symbol transition features upon which many symbol timing synchronizations schemes depend. Related to this is the problem that the effects of carrier phase error are difficult to separate from symbol timing error in CPM and OQPSK signals. Since the phase of the carrier is unknown, either the in-phase or the quadrature data stream in the demodulator is blindly delayed. The symbols are not yet in phase alignment, so there tends to be mixing with nearby symbols and phases. The present invention is directed to providing a phase and timing error when multiple symbols influence the data samples.